Cali this is awful for you, and I totally respect your concern for the children if you leave. The current situation gives your AP no incentive to stop drinking, as you've seen from the scenes over buying alcohol. It may take you leaving the picture before she if forced to seek help, although there are no guarantees.
Does she have a family or other support network if you move on your own, including the children's father? Think about the disruption of the move, especially for the children, with their mother's drinking undiminished. It sounds unworkable. Also, be wary of any promises on her part to change. It's not easy for an A to stop drinking, and doing it under threat doesn't always produce the best result.